Why is not enough to copy the node configuration from an object to another to texture the object A the same as the object B?
Head B has different UV map then the head A. That's why you can't use the same texture and expect to get the same result. To fix this problem, you should bake head A texture to head B. If material of Head A consists of few different textures (f.ex. color, normal, glossy etc.) you should each of this textures in head A material, (one by one-different texture for each bake) connect to Diffuse BSDF and straight to Material Output and bake Diffuse Color on new texture for head B. From the node setup, that you have on the images uploaded, it's obvious though, that you are using only Color texture (the rest of the nodes is useless in your setup), so you need to bake only one texture. Your head B need to have only one material added. If there will be more materials, you would have to add Image Texture node with the new texture added to each of the materials. Otherwise you'll get an error and bake will fail.